Special counsel Robert S. Mueller III is likely to be interested in Jared Kushner’s evolving disclosure of foreign contacts during the security clearance process, legal analysts said, and it is possible that the president’s son-in-law could be in legal jeopardy for not fully detailing the interactions from the start.

Kushner, one of President Trump’s closest advisers, has filed three updates to his national security questionnaire since submitting it in mid-January, according to people familiar with the matter. That is significant because the document — known as an SF-86 — warns that those who submit false information could be charged with a federal crime and face up to five years in prison.

Prosecutions for filing erroneous SF-86 forms are rare — though the Justice Department has brought cases against those with intentional omissions, and people have been denied security clearance for incorrect forms, legal analysts said.

Under the microscope of Mueller’s investigation, the analysts said, Kushner’s mistakes might be viewed as evidence that Kushner met with Russian officials, then tried to keep anyone from finding out. His representatives contend that the omissions were honest errors that were corrected quickly.

“Mueller’s task is examining whether he thinks there’s evidence that this was not simply a mistake or an oversight, but was actually a deliberate attempt to conceal these contacts,” said Randall Eliason, a former federal prosecutor who specializes in public corruption and government fraud. “And if that’s the case, that’s definitely potentially a crime.”

The SF-86 is a 127-page form that requests voluminous information about a person’s employment history, finances, family, travel and other matters. The form asks several questions about foreign contacts, requiring applicants to list any “close and/or continuing contact with a foreign national within the last seven years,” along with any contact with a representative of a foreign government.

The form is a part of a person’s background check for certain federal jobs and is meant to ascertain whether the person can be awarded a security clearance.

Legal analysts said it is not uncommon for people to forget information; nor is it uncommon for officials to encounter difficulty in the security clearance process.

Kushner’s national security questionnaire was first submitted on Jan. 18, though a person familiar with his account said that his office did so prematurely, and the form did not list his foreign contacts and got the dates of his graduate degrees and his father-in-law’s address wrong.

The next day, Kushner’s representatives submitted an addendum acknowledging that he had foreign contacts and saying that he would willingly detail them, the person said.

At the time, Kushner’s representatives had not compiled a list of the contacts, but they did so and submitted another addendum with them in mid-May, before an interview with FBI background investigators, the person said. The addendum detailed more than 100 calls or meetings with representatives of more than 20 countries, most of which came during the presidential transition, according to Jamie Gorelick, one of Kushner’s attorneys.

“Jared was trying to be fully compliant and upfront and transparent in this process, and when he learned that the document had been prematurely submitted, he was very clear that we should correct the record on that,” Gorelick said.

On June 21, Kushner submitted another addendum; this one listed the meeting he attended — along with Donald Trump Jr. and Paul Manafort, Donald Trump’s campaign manager at the time — with a Russian lawyer who Trump Jr. believed had damaging information about Hillary Clinton.

A person close to Kushner said he did not remember the meeting with the lawyer, Natalia Veselnitskaya, when submitting his list of foreign contacts in mid-May. The person said his lawyers discovered correspondence about it while reviewing emails to turn over information to congressional investigators. Gorelick said the meeting was included “out of an abundance of caution.”

“As Mr. Kushner has consistently stated, he is eager to cooperate and share what he knows,” Gorelick said.

Mark Zaid, a national security lawyer, said he believes that a disclosure of the meeting would not have been required, because Veselnitskaya is not now a government lawyer and Kushner does not have a close or continuing relationship with her.

“Too many people are imposing requirements on him that don’t exist,” Zaid said. The person familiar with Kushner’s account said he was interviewed by the FBI after supplementing his disclosure in June. The agents interviewing him were doing so as part of the background check process, the person said. It is unclear if Kushner also was approached by Mueller’s office.

Still, Zaid said that Kushner’s earlier, flawed SF-86 form was “problematic,” and that if “Jared Kushner were just Jared Simpson who was up for a job at the Defense Department, he would be in much hotter water with respect to an agency adjudicating his clearance based on his Russian contacts.”

If prosecutors were to try to bring charges against Kushner connected to his filings, they would have to prove that his omissions were intentional. Earlier this year, a former Drug Enforcement Administration agent was sentenced to one year of probation in a case in which he and a colleague were convicted of lying about their employment at an adult entertainment club and their relationship with a Brazilian national who danced there. The prosecution was led in part by Andrew D. Goldstein, then an assistant U.S. attorney in the Southern District of New York. He has since joined Mueller’s team.

Attorney General Jeff Sessions also indicated on a security clearance form that he had not had any contact with a foreign government official — even though he met with Sergey Kislyak, the Russian ambassador to the United States, twice last year. An aide said that he was told by the FBI investigator handling the background check that Sessions need not list meetings with foreign dignitaries in connection with Senate activities.

Edward B. MacMahon Jr., another national security lawyer in private practice, said he “can’t imagine there’s a risk of prosecution” with Kushner.

“If you’re under scrutiny, and you have electronic records that can help you fill these out to put an end to the questions, you might just do that,” MacMahon said. “Somebody will say that means you were hiding something, and somebody will say that means you were being more forthcoming. It depends on whose ox is being gored.”

But Harry Litman, a former U.S. attorney and Justice Department official who was involved in discussions about the SF-86 form many years ago, said Kushner probably fears that there is “real jeopardy” from the special counsel, and that explains his updates to his form.

“As a result of the Mueller investigation, there’s broader goals in play,” Litman said, “and certainly his lawyers are advising him, ‘Look, the game has changed here.’ ”